Module 40: Item Fit Statistics for Item Response Theory Models

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Drawing valid inferences from item response theory (IRT) models is contingent upon a good fit of the data to the model. Violations of model-data fit have numerous consequences, limiting the usefulness and applicability of the model. This instructional module provides an overview of methods used for evaluating the fit of IRT models. Upon completing this module, the reader will have an understanding of traditional and Bayesian approaches for evaluating model-data fit of IRT models, the relative advantages of each approach, and the software available to implement each method.

Keywords: Bayesian statistics, estimation, item response theory, IRT, Markov chain Monte Carlo, MCMC, model fit, posterior distribution, posterior predictive checks

Allison J. Ames

Assistant Professor

Allison is an assistant professor in the Educational Statistics and Research Methods program in the Department of Rehabilitation, Human Resources and Communication Disorders, Research Methodology, and Counseling at the University of Arkansas. There, she teaches courses in educational statistics, including a course on Bayesian inference. Allison received her Ph.D. from the University of North Carolina at Greensboro. Her research interests include Bayesian item response theory, with an emphasis on prior specification; model-data fit; and models for response processes. Her research has been published in prominent peer-reviewed journals. She enjoyed collaborating on this project with a graduate student, senior faculty member, and the Instructional Design Team.
Contact Allison via boykin@uark.edu

Randall D. Penfield

Professor, Educational Research Methodology, University of North Carolina at Greensboro, NC

Dr. Penfield is Dean of the School of Education and a Professor of educational measurement and assessment. His research focuses on issues of fairness in testing, validity of test scores, and the advancement of methods and statistical models used in the field of assessment. In recognition of his scholarly productivity he was awarded the 2005 early career award by the National Council on Measurement in Education, and was named a Fellow of the American Educational Research Association in 2011. In addition, he has served as co-principal investigator or consultant on a numerous federal grants funded by the National Science Foundation and the Department of Education.